Author | Lint, J. H. van. author |
---|---|
Title | Introduction to Coding Theory [electronic resource] / by J. H. van Lint |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-662-00174-5 |
Descript | XII, 186 p. 11 illus. online resource |
1 Mathematical Background -- 1.1. Algebra -- 1.2. Krawtchouk Polynomials -- 1.3. Combinatorial Theory -- 1.4. Probability Theory -- 2 Shannonโs Theorem -- 2.1. Introduction -- 2.2. Shannonโs Theorem -- 2.3. Comments -- 2.4. Problems -- 3 Linear Codes -- 3.1. Block Codes -- 3.2. Linear Codes -- 3.3. Hamming Codes -- 3.4. Majority Logic Decoding -- 3.5. Weight Enumerators -- 3.6. Comments -- 3.7. Problems -- 4 Some Good Codes -- 4.1. Hadamard Codes and Generalizations -- 4.2. The Binary Golay Code -- 4.3. The Ternary Golay Code -- 4.4. Constructing Codes from Other Codes -- 4.5. Reed-Muller Codes -- 4.6. Kerdock Codes -- 4.7. Comments -- 4.8. Problems -- 5 Bounds on Codes -- 5.1. Introduction: The Gilbert Bound -- 5.2. Upper Bounds -- 5.3. The Linear Programming Bound -- 5.4. Comments -- 5.5. Problems -- 6 Cyclic Codes -- 6.1. Definitions -- 6.2. Generator Matrix and Check Polynomial -- 6.3. Zeros of a Cyclic Code -- 6.4. The Idempotent of a Cyclic Code -- 6.5. Other Representations of Cyclic Codes -- 6.6. BCH Codes -- 6.7. Decoding BCH Codes -- 6.8. Reed-Solomon Codes and Algebraic Geometry Codes -- 6.9. Quadratic Residue Codes -- 6.10. Binary Cyclic codes of length 2n (n odd) -- 6.11. Comments -- 6.12. Problems -- 7 Perfect Codes and Uniformly Packed Codes -- 7.1. Lloydโs Theorem -- 7.2. The Characteristic Polynomial of a Code -- 7.3. Uniformly Packed Codes -- 7.4. Examples of Uniformly Packed Codes -- 7.5. Nonexistence Theorems -- 7.6. Comments -- 7.7. Problems -- 8 Goppa Codes -- 8.1. Motivation -- 8.2. Goppa Codes -- 8.3. The Minimum Distance of Goppa Codes -- 8.4. Asymptotic Behaviour of Goppa Codes -- 8.5. Decoding Goppa Codes -- 8.6. Generalized BCH Codes -- 8.7. Comments -- 8.8. Problems -- 9 Asymptotically Good Algebraic Codes -- 9.1. A Simple Nonconstructive Example -- 9.2. Justesen Codes -- 9.3. Comments -- 9.4. Problems -- 10 Arithmetic Codes -- 10.1. AN Codes -- 10.2. The Arithmetic and Modular Weight -- 10.3. Mandelbaum-Barrows Codes -- 10.4. Comments -- 10.5. Problems -- 11 Convolutional Codes -- 11.1. Introduction -- 11.2. Decoding of Convolutional Codes -- 11.3. An Analog of the Gilbert Bound for Some Convolutional Codes -- 11.4. Construction of Convolutional Codes from Cyclic Block Codes -- 11.5. Automorphisms of Convolutional Codes -- 11.6. Comments -- 11.7. Problems -- Hints and Solutions to Problems -- References